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Physics-

General

Easy

Question

What is the equivalent resistance between $A blank a n d blank B$ in the given circuit?

$4 Ω$
$2 Ω$
$\frac{8}{3} Ω$
$\frac{3}{8} Ω$

The correct answer is: $fraction numerator 8 over denominator 3 end fraction capital omega$

$R subscript 1 end subscript$ and $R subscript 2 end subscript$ are in series
$therefore blank R subscript 12 end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript equals 4 capital omega$

$R subscript 12 end subscript a n d R subscript 3 end subscript$ are in parallel
$R subscript 123 end subscript equals fraction numerator R subscript 3 end subscript cross times R subscript 12 end subscript over denominator R subscript 3 end subscript plus R subscript 12 end subscript end fraction$
$equals fraction numerator 4 cross times 4 over denominator 4 plus 4 end fraction$
$equals 2 capital omega$
$R subscript 123 end subscript$ and $R subscript 4 end subscript$ are in series
$therefore blank R subscript 1234 end subscript equals R subscript 123 end subscript plus R subscript 4 end subscript$
$equals 2 capital omega plus 2 capital omega$
$equals 4 capital omega$
$R subscript 1234 end subscript$ and $R subscript 5 end subscript$ are in parallel
$therefore R subscript 12345 end subscript equals 2 capital omega$
$R subscript 12345 end subscript$ and $R subscript 6 end subscript$ are in series
$2 capital omega plus 2 capital omega equals 4 capital omega$
$equals R subscript 123456 end subscript$
Now, $R subscript 123456 end subscript$ and $R subscript 7 end subscript$ are in parallel
$therefore R subscript c o m b end subscript equals fraction numerator 4 cross times 8 over denominator 4 plus 8 end fraction$
$equals fraction numerator 32 over denominator 12 end fraction equals fraction numerator 8 over denominator 3 end fraction capital omega$

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